I do believe there would be a strong market push for simplicity, and most customers would not want to perform a complex bidding operation like this. However, a free market would allow providers to experiment with it. The pricing models that customers like would quickly become the winners.

I don't actually think there would be a really serious variability in the real cost, since the base cost is fairly clear -- a low-skilled worker's time and a vehicle cost per mile, plus accounting for time and miles spent idle/driving empty. In an efficient market, profits would remain in a modest zone and the cost will get close to this. Variation in price would come instead from innovation -- such as really good jitney service, better placement of cabs to be close to expected customers, more efficient use of idle time.

Other possible ideas include merging with package delivery. In many cases you could provide door to door service for humans who don't even know you are also carrying some less-impatient packages along roughly the same path. Even if the cab makes stops for package handoff those would be brief and need never take the passenger off her shortest route. This is also greatly facilitated by planning based on knowing the destination point.

There's also the potential for good use of pre-planning. People at a theatre can reliably inform their taxi dispatcher they will want a cab from the theatre to home hours in advance. Even people in shopping and meetings can usually make predictions that they will be leaving "in 10 minutes" or even pre-enter their route and an approximate time, then update the time with quick notes.

Note there is one item of merit in the anti-congestion argument. Today's taxis spend time idle, driving around. This is not something private cars do. More idle taxis does mean more congestion and more pollution, so you don't want an oversupply. However, my plan eliminates this concern, because idle taxis -- especially if they are hybrid or electric -- would sit parked, with gasoline engine off. In fact this may be the most compelling argument to the public for ending the hailing system -- calculate just how much gasoline is burned having taxis roam the streets looking for hails.